glamrockqueen7

2021-08-20

To calculate: The product of $[x-(3-\sqrt{5})][x-(3+\sqrt{5})]$

Demi-Leigh Barrera

Skilled2021-08-21Added 97 answers

Step 1

Formula used:

$(a+b)(a-b)={a}^{2}-{b}^{2}$

$(a-b)}^{2}={a}^{2}-2ab+{b}^{2$

Associative property,$(a+b)+c=a+(b+c)$

Step 2

If P (x) represent the given expression, then

$P\left(x\right)=[x-(3-\sqrt{5})][x-(3+\sqrt{5})]$

$P\left(x\right)=(x-3+\sqrt{5})(x-3-\sqrt{5})$

Use associative property of algebraic expressions,

Associative property is written as,

$(a+b)+c=a+(b+c)$

This property modifies the expression to,

$P\left(x\right)=((x-3)+\sqrt{5})((x-3)-\sqrt{5})$

Apply arithmetic rule:

$(a+b)(a-b)={a}^{2}-{b}^{2}$

Here,$a=(x-3),\text{}b=\left(\sqrt{5}\right)$

Hence,

$P\left(x\right)={(x-3)}^{2}-{\left(\sqrt{5}\right)}^{2}Z$

Apply arithmetic rule:

$(a-b)}^{2}={a}^{2}-2ab+{b}^{2$

Here,$a=x,\text{}b=3$

Hence,

$P\left(x\right)={(x-3)}^{2}-{\left(\sqrt{5}\right)}^{2}$

$={x}^{2}-6x+9-5$

$={x}^{2}-6x+4$

Hence, the product of$[x-(3-\sqrt{5})][x-(3+\sqrt{5})]$ is ${x}^{2}-6x+4$

Formula used:

Associative property,

Step 2

If P (x) represent the given expression, then

Use associative property of algebraic expressions,

Associative property is written as,

This property modifies the expression to,

Apply arithmetic rule:

Here,

Hence,

Apply arithmetic rule:

Here,

Hence,

Hence, the product of

Jeffrey Jordon

Expert2022-07-07Added 2605 answers

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